1. Lesson 4

Mathematics 20-1 Module 7

Module 7: Absolute Value and Reciprocal Functions

 

Lesson 4: Reciprocal Functions

 
Focus

 

This shows an illustration of an artwork that is similar to that of M.C. Escher.

iStockphoto/Thinkstock

M. C. Escher was a Dutch graphic artist whose works were mathematically inspired. Though Escher himself was not trained in mathematics, he seemed to have an intuitive understanding of geometry and plane symmetry. While he created pieces on various themes throughout his career, Escher is perhaps best known for his depictions of impossible reality. The image here, though not by Escher, is remarkably similar to his lithograph Relativity. Another one of his works that exhibits this theme is Still Life and Street. You may want to search the Internet for these and other examples of M. C. Escher’s lithographs and woodcuts.

 

In this lesson you will explore reciprocal functions. Graphing reciprocal functions is similar to creating a work of art. The graph of the reciprocal of a function is very different from the graph of the original function. Like the artworks of Escher, however, the basis of creating the graph is mathematical.

 

Outcomes

 

At the end of this lesson you will be able to

  • compare the graph of  to the graph of y = f(x)
  • identify, given a function f(x), values of x for which  will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression
  • graph, with or without technology, , given y = f(x) as a function or a graph, and explain the strategies used
  • graph, with or without technology, y = f(x), given  as a function or a graph, and explain the strategies used
Lesson Questions

 

In this lesson you will investigate the following questions:

  • How are the properties of reciprocals related to the properties of reciprocal functions?

  • What are the strategies for graphing the reciprocal of a function?
Assessment

 

Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 4 Assignment (Download the Lesson 4 Assignment and save it in your course folder now.)

  • course folder submissions from Try This and Share activities

  • additions to Module 7 Glossary Terms and Formula Sheet

  • work under Project Connection
Materials and Equipment

 

You will need a graphing calculator and graph paper.